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A126164
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Sum of the proper exponential divisors of n.
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15
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0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 10, 0, 0, 0, 6, 5, 0, 3, 14, 0, 0, 0, 2, 0, 0, 0, 36, 0, 0, 0, 10, 0, 0, 0, 22, 15, 0, 0, 18, 7, 10, 0, 26, 0, 6, 0, 14, 0, 0, 0, 30, 0, 0, 21, 14, 0, 0, 0, 34, 0, 0, 0, 48, 0, 0, 15
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OFFSET
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1,4
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COMMENTS
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The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
Ant King, Mathematica programs for A126164 - A126166
Eric Weisstein's World of Mathematics, e-Divisor.
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FORMULA
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a(n) = esigma(n) - n = A051377(n) - n.
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EXAMPLE
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The exponential divisors of 240 are 30, 60 and 240, so a(240) = 30+60 = 90.
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PROG
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(PARI)
A051377(n) = { my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d)); }; \\ This function from Charles R Greathouse IV, Nov 22 2011
A126164(n) = (A051377(n) - n); \\ Antti Karttunen, Oct 04 2017, after the given formula
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CROSSREFS
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Cf. A051377, A049419, A054979, A054980, A126168.
Sequence in context: A263145 A057108 A063958 * A340317 A145007 A308376
Adjacent sequences: A126161 A126162 A126163 * A126165 A126166 A126167
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KEYWORD
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easy,nonn
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AUTHOR
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Ant King, Dec 21 2006
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STATUS
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approved
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